Related papers: Semi-Random Sparse Recovery in Nearly-Linear Time
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\ell_\infty$ error guarantees.…
Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…
Dantzig selector (DS) and LASSO problems have attracted plenty of attention in statistical learning, sparse data recovery and mathematical optimization. In this paper, we provide a theoretical analysis of the sparse recovery stability of…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…